Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and strong kernel

Abstract

Since the stochastic bifurcation theory is still in its infancy, we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model. Thus, this paper mainly focuses on studying the stochastic bifurcation of a stochastic logistic model with distributed delay in the strong kernel case, which is affected by noise. Therefore, we use the intrinsic growth rate as a bifurcation parameter. First, we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model. Furthermore, by deriving the corresponding Fokker–Planck equation, we obtain the expression of the joint density function of the stochastic logistic system near the positive equilibrium point. Finally, some conclusions are given.